Details

analyze1.2s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
26.5%	72.9%	0.5%	9
38.2%	60.7%	1.1%	10
41.7%	54.9%	3.4%	11
47.6%	47.4%	5%	12
53.4%	39.4%	7.2%	13
54.9%	34.5%	10.6%	14

sample70.0ms

Algorithm

intervals

Results

22.0ms	201×	body	80	valid
9.0ms	19×	body	1280	valid
7.0ms	20×	body	640	valid
4.0ms	47×	body	80	invalid
4.0ms	12×	body	320	valid
3.0ms	8×	body	640	invalid
2.0ms	5×	body	1280	invalid
2.0ms	9×	body	320	invalid
1.0ms	5×	body	160	invalid
1.0ms	4×	body	160	valid

simplify69.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4845	16
1	4845	16

prune14.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 27.7b

Counts

2 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

0.9b	(/ (cos (* 2.0 x)) (* x (* x (* (pow c 2.0) (pow s 2.0)))))
5.5b	(* x (* x (* (pow c 2.0) (pow s 2.0))))
8.1b	(* x (* (pow c 2.0) (pow s 2.0)))
15.5b	(* (pow c 2.0) (pow s 2.0))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

122×	`add-exp-log`
88×	`prod-exp`
34×	`add-cbrt-cube`
24×	`add-sqr-sqrt` `pow-to-exp` `pow-exp`
16×	`cbrt-unprod`
13×	`associate-l`
12×	`add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity` `div-exp`
11×	`pow1`
9×	`associate-r` `unswap-sqr`
8×	`sqr-pow`
5×	`pow-prod-down`
4×	`cbrt-undiv` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l`
1×	`frac-2neg` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 128

Calls

4 calls:

11.0ms	(/ (cos (* 2.0 x)) (* x (* x (* (pow c 2.0) (pow s 2.0)))))
9.0ms	(* x (* x (* (pow c 2.0) (pow s 2.0))))
7.0ms	(* x (* (pow c 2.0) (pow s 2.0)))
7.0ms	(* (pow c 2.0) (pow s 2.0))

series262.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ (cos (* 2.0 x)) (* x (* x (* (pow c 2.0) (pow s 2.0)))))
62.0ms	(* x (* x (* (pow c 2.0) (pow s 2.0))))
56.0ms	(* x (* (pow c 2.0) (pow s 2.0)))
59.0ms	(* (pow c 2.0) (pow s 2.0))

simplify74.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4952	1811
1	4952	1811

prune274.0ms

Filtered

82 candidates to 140 candidates (-70.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	128	12	140
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	129	13	142

Merged error: 10.0b

Counts

142 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (* c s) 2.0)
0.9b	(/ (cos (* 2.0 x)) (* x (* x (pow (* c s) 2.0))))
5.5b	(* x (* x (pow (* c s) 2.0)))
8.1b	(* x (pow (* c s) 2.0))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-exp-log`
26×	`prod-exp`
20×	`add-cbrt-cube`
13×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1`
8×	`pow-exp`
7×	`cbrt-unprod`
6×	`div-exp` `associate-r` `associate-l`
4×	`pow-to-exp` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `times-frac` `associate-/l*` `sqr-pow`
2×	`unpow-prod-down` `pow-pow` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`frac-2neg` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 86

Calls

4 calls:

4.0ms	(pow (* c s) 2.0)
8.0ms	(/ (cos (* 2.0 x)) (* x (* x (pow (* c s) 2.0))))
5.0ms	(* x (* x (pow (* c s) 2.0)))
5.0ms	(* x (pow (* c s) 2.0))

series193.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(pow (* c s) 2.0)
69.0ms	(/ (cos (* 2.0 x)) (* x (* x (pow (* c s) 2.0))))
58.0ms	(* x (* x (pow (* c s) 2.0)))
48.0ms	(* x (pow (* c s) 2.0))

simplify50.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4963	1115
1	4963	1115

prune210.0ms

Filtered

62 candidates to 98 candidates (-58.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	90	8	98
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	98	13	111

Merged error: 5.0b

Counts

111 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2)))
0.9b	(/ (cos (* 2.0 x)) (* x (* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2)))))
4.8b	(* x (pow (* c s) (* 1/2 2.0)))
5.5b	(* x (* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

247×	`add-exp-log`
182×	`prod-exp`
56×	`pow-exp`
34×	`add-cbrt-cube`
28×	`pow-to-exp`
22×	`div-exp`
16×	`cbrt-unprod`
13×	`add-sqr-sqrt`
11×	`associate-r`
10×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-l`
6×	`pow1`
4×	`cbrt-undiv` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l` `sqr-pow`
2×	`unpow-prod-down` `unswap-sqr`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 139

Calls

4 calls:

8.0ms	(* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2)))
11.0ms	(/ (cos (* 2.0 x)) (* x (* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2)))))
5.0ms	(* x (pow (* c s) (* 1/2 2.0)))
11.0ms	(* x (* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2))))

series228.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2)))
71.0ms	(/ (cos (* 2.0 x)) (* x (* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2)))))
51.0ms	(* x (pow (* c s) (* 1/2 2.0)))
56.0ms	(* x (* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2))))

simplify62.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4918	1843
1	4918	1843

prune236.0ms

Filtered

65 candidates to 151 candidates (-132.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	144	7	151
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	149	15	164

Merged error: 2.5b

Counts

164 → 15

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (* (pow (pow c (neg 1.0)) 1.0) (pow (pow s (neg 1.0)) 1.0)))
0.9b	(/ (cos (* 2.0 x)) (* x (* (* x (pow (/ 1 (* (pow (pow c (neg 1.0)) 1.0) (pow (pow s (neg 1.0)) 1.0))) 1.0)) (pow (* c s) (/ 2.0 2)))))
4.8b	(* x (pow (/ 1 (* (pow (pow c (neg 1.0)) 1.0) (pow (pow s (neg 1.0)) 1.0))) 1.0))
5.5b	(* x (* (* x (pow (/ 1 (* (pow (pow c (neg 1.0)) 1.0) (pow (pow s (neg 1.0)) 1.0))) 1.0)) (pow (* c s) (/ 2.0 2))))

rewrite241.0ms

Algorithm

rewrite-expression-head

Rules

3596×	`add-exp-log`
2957×	`prod-exp`
2239×	`pow-exp`
850×	`div-exp`
773×	`pow-to-exp`
260×	`rec-exp` `1-exp`
34×	`add-cbrt-cube`
18×	`add-sqr-sqrt`
14×	`cbrt-unprod`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`associate-r`
9×	`times-frac`
8×	`unpow-prod-down`
7×	`pow1`
6×	`cbrt-undiv` `associate-l` `associate-/l*`
4×	`add-log-exp`
3×	`div-inv` `unswap-sqr`
2×	`pow-flip` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `sqr-pow`
1×	`inv-pow`

Counts

4 → 903

Calls

4 calls:

12.0ms	(/ 1 (* (pow (pow c (neg 1.0)) 1.0) (pow (pow s (neg 1.0)) 1.0)))
48.0ms	(/ (cos (* 2.0 x)) (* x (* (* x (pow (/ 1 (* (pow (pow c (neg 1.0)) 1.0) (pow (pow s (neg 1.0)) 1.0))) 1.0)) (pow (* c s) (/ 2.0 2)))))
16.0ms	(* x (pow (/ 1 (* (pow (pow c (neg 1.0)) 1.0) (pow (pow s (neg 1.0)) 1.0))) 1.0))
34.0ms	(* x (* (* x (pow (/ 1 (* (pow (pow c (neg 1.0)) 1.0) (pow (pow s (neg 1.0)) 1.0))) 1.0)) (pow (* c s) (/ 2.0 2))))

series354.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ 1 (* (pow (pow c (neg 1.0)) 1.0) (pow (pow s (neg 1.0)) 1.0)))
109.0ms	(/ (cos (* 2.0 x)) (* x (* (* x (pow (/ 1 (* (pow (pow c (neg 1.0)) 1.0) (pow (pow s (neg 1.0)) 1.0))) 1.0)) (pow (* c s) (/ 2.0 2)))))
71.0ms	(* x (pow (/ 1 (* (pow (pow c (neg 1.0)) 1.0) (pow (pow s (neg 1.0)) 1.0))) 1.0))
98.0ms	(* x (* (* x (pow (/ 1 (* (pow (pow c (neg 1.0)) 1.0) (pow (pow s (neg 1.0)) 1.0))) 1.0)) (pow (* c s) (/ 2.0 2))))

simplify276.0ms

Algorithm

egg-herbie

Counts

915 → 915

Iterations

Useful iterations: 0 (152.0ms)

Iter	Nodes	Cost
0	5074	21442

prune331.0ms

Filtered

76 candidates to 915 candidates (-1103.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	908	7	915
Fresh	3	11	14
Picked	1	0	1
Done	0	0	0
Total	912	18	930

Merged error: 2.5b

Counts

930 → 18

regimes809.0ms

Accuracy

-1.9% (3.5b remaining)

Error of 5.9b against oracle of 2.4b and baseline of 5.8b

bsearch122.0ms

Steps

Iters	Range		Point
7	3.384254494171695e-133	2.492530660697105e-131	4.522624911795082e-133
11	-6.218673475875139e-83	-1.8963091445535583e-103	-2.6106778390028078e-89

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	56	67
1	56	67

end0.0ms

sample2.0s

Algorithm

intervals

Results

572.0ms	6038×	body	80	valid
330.0ms	663×	body	1280	valid
270.0ms	723×	body	640	valid
166.0ms	1830×	body	80	invalid
103.0ms	388×	body	320	valid
90.0ms	256×	body	640	invalid
73.0ms	145×	body	1280	invalid
52.0ms	198×	body	320	invalid
34.0ms	188×	body	160	valid
18.0ms	105×	body	160	invalid

Details

analyze1.2s

sample70.0ms

simplify69.0ms

prune14.0ms

localize14.0ms

rewrite43.0ms

series262.0ms

simplify74.0ms

prune274.0ms

localize15.0ms

rewrite24.0ms

series193.0ms

simplify50.0ms

prune210.0ms

localize18.0ms

rewrite42.0ms

series228.0ms

simplify62.0ms

prune236.0ms

localize27.0ms

rewrite241.0ms

series354.0ms

simplify276.0ms

prune331.0ms

regimes809.0ms

bsearch122.0ms

simplify2.0ms

end0.0ms

sample2.0s

Profiling